Both the English and Scottish football associations have lobbied Fifa for their teams to be allowed to wear embroidered poppies when they play each other at Wembley on Armistice Day.
Fifa has previously blocked the request, citing rules that prohibit the promotion of political or religious messages at matches, and has indicated it is set to maintain that position.
May said: “I think the stance that’s been taken by Fifa is utterly outrageous. Our football players want to recognise and respect those who have given their lives for our safety and security. I think it is absolutely right that they should be able to do so.”
Speaking during Prime Minister’s Questions on Wednesday, she added of the scandal-hit governing body: “I have to say to Fifa that before they start telling us what to do, they jolly well ought to sort their own house out.”
Wales are also seeking permission to wear poppies for their match against Serbia, which falls on 12 November, a day after the England-Scotland World Cup qualifying fixture.
England agreed to a compromise measure of wearing armbands with poppies on them when they played Spain in a friendly on 12 November 2011.